The above diagram shows the relationship between the pressure (\(y\)-axis) and the volume (\(x\)-axis) of an ideal gas when it changes its state in the order \(A \to B \to C \to D \to A.\) The processes \(A \to B\) and \(C \to D\) are isobaric processes with pressures \(2P\) and \(P,\) respectively. The processes \(B \to C\) and \(D \to A\) are isothermal processes with temperatures \(2T\) and \(T,\) respectively. Which of the following statements is correct?

a) The volume of the gas at state \(C\) is \(4\) times as large as that at state \(A.\)

b) The volume of the gas at state \(B\) is greater than that at state \(D.\)

c) The average speed of the molecules at state \(C\) is \(2\) times as large as that at state \(A.\)

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